The number of real value of $x$ for which $sin 2 x + sin 4 x = 2$ is ?

0

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1

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infinite

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none of these

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Solution

The correct option is A $0$
As the maximum value of $sin x$ is $1$ , for the given sum to be $2$ , both $sin 2 x$ and $sin 4 x$ must be 1.
$∴ 2 x = (4 n + 1) \frac{π}{2}$ $(n \in Z)$
But then, $4 x = (4 n + 1) π ⟹ sin 4 x = 0$
Therefore, there is no solution as it is not possible for $sin 2 x$ and $sin 4 x$ to be $1$ at the same time for any $x$ .

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